As used herein, dispersive mixing refers to the breakup and reduction in size of regions of inhomogeneity, such as gels, agglomerates, or regions of high viscosity and low molecular diffusivity, within a matrix of another material. During dispersive mixing, stresses must be applied to the surfaces of the regions of inhomogeneity in order to break them up. Dispersive mixing may involve miscible or immiscible systems, and even in a system where the components are thermodynamically miscible with one another, dispersive mixing may be required from the viewpoint of kinetics if the time scale to molecularly distribute one component in the other is very long. Dispersive mixing is advantageous in that it results in smaller particles or regions of one material in a matrix of another material, generating more surface area for interfacial bonding and better homogeneity, which often gives rise to improved physical and/or processing properties in the overall material. The dispersive mixing process is carried out until the particles or regions are sufficiently small so that any further breakup leads to little effective change in properties of the system.
Other terms for mixing are employed. Two such terms are distributive mixing and blending. Distributive mixing is the rearrangement of the relative positions of phases or regions without significant change in their sizes. Often it is important to have good distributive mixing for the improvement of appearance and other physical properties of a mixed material.
Blending involves both the break up of inhomogeneous regions by dispersive mixing and position rearrangement by distributive mixing. In an important sense, blending may be thought of as combining a change in size process with a distribution process. However, when blending two or more components of the same viscosity that are thermodynamically identical, changes in the sizes of regions of inhomogeneity readily take place so that consideration of stresses at the interface between the different components is not required.
Of particular interest to the polymer industry is the dispersive mixing of a high molecular weight polymer in a lower molecular weight polymer matrix. Bimodal molecular weight distribution polymer products are often made this way. In this case, the components being mixed are of the same basic chemical type and successful dispersive mixing can result in improved melt strength, giving rise to improved processing characteristics. However, dispersive mixing of such materials is especially difficult because it is difficult to transmit stresses to a high viscosity minor phase through a surrounding matrix of low viscosity material. Known mixing processes possess only limited ability to accomplish this.
It is believed by those skilled in the art that with viscoelastic materials, high deformation rates relative to the relaxation time of the minor phase and the matrix will allow more effective transmission of stress to the minor phase. Applicant also believes that at a high deformation rate, the minor phase is more likely to fail at lower strains and thus disperse more effectively. The measure of the relaxation time of the material relative to the time scale of the deformation is known in rheology as the Deborah Number (Principles of Polymer Processing, by Z. Tadmor and C. Gogos, John Wiley and Sons, 1979). For extensional deformations, the Deborah Number is given by the formula: .lambda./(L/(v2-v1)), wherein .lambda. is the effective relaxation time of the material, L is the length over which the material is deformed, and (v2-v1) is the change in the velocity of the material as it is deformed.
While the relative rate of deformation (i.e. the Deborah Number) is important for optimizing a dispersive mixing process, so too is the total deformation of the material, since the failure of regions under deformation usually requires that a minimum deformation be exceeded. A measure of the amount of deformation in extensional flow is known as the Hencky Strain measure. A description of the Hencky Strain can be found in the text Rheology, Principles, Measurements, and Applications by C. W. Macosko (VCH, 1994). The formal definition of Hencky Strain is the natural logarithm of the final length of the sample divided by the initial length. For purposes of the present invention, an approximation of Hencky strain is used: the natural log of the area of the flow entering a convergent geometry divided by the smallest area of the geometry for a substantially extensional flow field.
A majority of mixing processes known in the art, such as those done with batch mixers made by Banbury and Steward-Bolling, continuous mixers such as the twin screw mixers of Welding Engineers and Werner & Pfleiderer, and the intensive continuous mixers of Farrell Corporation (FCM) and Kobe Steel (LCM), employ the rotating action of a screw or rotors as the major energy input to the system to mix materials. Because of such rotating action, these processes subject materials to a high level of shear flows compared to extensional flows. The high levels of shear flows in these processes have two results. First, such processes are relatively energy inefficient in that shear flows contribute to significant energy dissipation and rapid heat rise in the system being mixed, thus often limiting the amount of mixing that is possible without degrading the material. See for example, L. Erwin, "Principles of Laminar Fluid/Fluid Mixing," Mixing in Polymer Processing, C. Rauwendaal, ed. (Marcel Dekker, Inc., 1991), in which it is noted that mixing processes that rely on simple shear flow require several orders of magnitude more energy than those that rely on extensional flow to achieve the same level of mixing. Second, the dispersive mixing capability based on the shear flow component of these mixing processes is poor. It is known that extensional flows, on the other hand, are much better at breaking up inhomogeneities in a material than shear flows and are therefore much better at dispersive mixing. It is the extensional flow capabilities of rotation-type mixing devices that contribute most effectively to the limited success of these devices as dispersive mixers.
For example, U.S. Pat. No. 4,417,350 describes the use of non-intermeshing two-wing rotors for use in high intensity, batch mixing machines. These rotors rotate side-by-side within the mixing machine. Although the patent states in the abstract, "b!y virtue of driving the rotors at synchronous speed with the phase angle relationship of about 180.degree., a powerful squeeze-flow mixing action and advantageous pull-down effect on the materials being mixed is produced twice during each cycle of rotation," in fact such rotors intermittently expose the materials being mixed to only a brief extensional stretch while imposing a high level of shear. The squeeze flow action is only incidental to the roll mill-type action of the rotors. Squeeze flow imparts a positive displacement to material between surfaces that approach one another, whereas the rotors in the above mentioned application drag the material through a gap.
U.S. Pat. No. 3,458,894 discloses a mixer comprising a barrel that is lined with a number of detachable plates. The mixer contains a mixer blade assembly having interrupted helical vanes or flights cast on sleeves that are mounted on a shaft. The shaft moves in both reciprocative and rotating directions. Bolts project as lugs into the mixing chamber in the area of the vane interruptions, such that the interrupted vanes clear the lugs during the rotational and reciprocative movement in a type of weaving pattern. Because the interrupted vanes clear the lugs during the rotational and reciprocative movement, very little squeeze flow, though some limited stretching flow, takes place with this apparatus. This device has been analyzed in "Modeling of the Cokneader," by Pierre H. M. Elemans, Chapter 12, Mixing and Compounding of Polymers--Theory and Practice, I. Manas-Zloczower and Z. Tadmor, eds. (Hanser/Gardner, 1994). Elemans notes that the "weaving pattern gives the cokneader an excellent distributive mixing quality." However, it lacks an excellent dispersive mixing capacity. And due to the rotational movement of the shaft and the vanes thereon, this assembly subjects the materials it mixes to a high degree of shear compared to extension.
Although such conventional, rotating-type mixing devices typically mix materials at reasonable Deborah Numbers, i.e., greater than about 10, the amount of extensional stretching relative to shear deformations that can be achieved in such devices is low. A key problem facing those intent on improving continuous mixing processes is how to achieve the combination of high stretching rates (Deborah Number) and high stretching (Hencky Strains) simultaneously in an energy efficient process.
Mixing processes employing squeeze flow are also known. For example, U.S. Pat. No. 2,828,111 discloses a plunger mixer or reactor comprising a closed cylindrical body member provided with spaced discs held in a fixed position with relation to each other and a plunger arranged to reciprocate through aligned holes in the discs, the plunger also carrying discs fixed in space relation thereon. The discs on the plunger and the discs in the body member are alternately arranged, and the plunger is adapted to move longitudinally in the cylindrical body. The device also comprises an openings through which material may be fed into and discharged from the body member.
This device is designed to provide a low degree of mixing as seen in the example where the holes constitute more than 20% of the total cross section area. This provides a Hencky strain of less than 2 under any condition of motion. The rate of reciprocating motion is 2 strokes per minute over a few inches, providing a Deborah number that appears to be much less than 10 under the conditions described for the use of this device.
Applicant has discovered that excellent dispersive mixing occurs when a viscoelastic material is subjected to primarily extensional flows at a high Hencky strain and a high Deborah Number in a reciprocating, squeeze flow device affording passes through narrow passages. In addition, preferably, more than 50% of the viscoelastic material is also subjected to a shear stress of at least about 35 psi in the device, thereby making the material susceptible to slip within the device. In contrast with known rotating-type mixing devices, in which slip of the material along the walls of the device is to be avoided, slip is beneficial in the present process. For flow through passages, the existence of slip along the wall shifts much of the wasted shear flow energy dissipation towards more energy efficient input into extensional flow deformation.
That the combination of squeeze flow, a Hencky strain greater than 2, and a mixing rate corresponding to a Deborah Number greater than 10 results in optimum dispersive mixing of viscoelastic material has gone until now unrecognized.